Lamb waves are a type of wave that may be propagated though a material, in a manner similar to sound waves propagating though a fluid. The direction of vibration of a particle within the material, as the wave propagates, classifies the type of wave. In particular, if the particle vibrates in a direction that is parallel with the surface of the material and in a direction that is perpendicular with the wave propagation direction, then the wave is a shear-horizontal wave. If the particle vibrates in it direction that is normal with the surface of the material and in the wave propagation direction, then the wave is a Lamb wave. The different types of waves will now be described with reference to FIG. 1.
FIG. 1 illustrates propagation of waves through a material 100.
As shown in the figure, material 100 has a top surface 101, has a thickness, T, and is positioned about a y-axis 102, an x-axis 104, a z-axis 106. A particle 108 is disposed within material 100. A wave generating component 103 and a receiving component 105 are disposed on top surface 101 a distance, d, from one another. Also shown on the left side of the figure is a plane 110 about particle 108, wherein plane 110 includes a y-axis 112, x-axis 104 and a z-axis 114. In plane 110, particle 108 vibrates between a direction indicated by arrow 116 and a direction indicated by arrow 118 as a wave propagates in a direction indicated by arrow 120 in the case of a shear-horizontal wave, wherein plane 110 includes y-axis 112, x-axis 104 and z-axis 114. In this portion of the figure, in plane 110, particle 108 vibrates between a direction indicated by arrow 122 and a direction indicated by arrow 124 as a wave propagates in a direction indicated by arrow 120.
Wave generating component 103 generates a Lamb wave for receiving component 105. Wave generating component 103 may be any type of electromechanical transducer that is operable to convert electrical energy to mechanical energy, a non-limiting example of which includes a piezoelectric device. Receiving component 105 is operable to detect a wave propagated from wave generating component 103.
Suppose that a wave generating component 103 induces vibrations in material 100 at top surface 101 near the position of particle 108. If the vibrations are of a sufficient frequency, waves will propagate from the point of particle 108 in many directions. For purposes of discussion, consider the waves in the direction indicated by arrow 120 toward the end of material 100 indicated by plane 128 having particle 126 therein. The waves will be detected by receiving component 105. Of these waves, two types are shown in the figure. A shear-horizontal wave is illustrated with reference to the lower left of the figure, whereas a Lamb wave is illustrated in with reference to the lower right of the figure. For the purposes of discussion, consider only the lamb waves.
A shear-horizontal wave is distinguishable from a Lamb wave by the vibrational direction of the particles within the material as the wave propagates. As shown in the figure, in a shear-horizontal wave, particle 108 vibrates in a direction parallel with top surface 101 and perpendicular to the direction 120 of the wave propagation. On the other hand, in a Lamb wave, particle 108 vibrates in a direction perpendicular with top surface 101 and parallel to the direction 120 of the wave propagation.
The present application is generally drawn to the use of Lamb waves in detecting a thickness of a material.
There are two types of Lamb waves, anti-symmetrical and symmetrical. The differences will be discussed with reference to FIG. 2.
FIG. 2 illustrates a view of plane 128 of material 100 of FIG. 1.
As shown in FIG. 2, a particle 200 moves in a positive direction in y-axis 112 and in a positive direction of x-axis 104, whereas a particle 202 moves in a negative direction in y-axis 112 and in a positive direction of x-axis 104. This is an example of symmetrical motion, wherein the symmetry is about the middle of the plane. On the other hand, a particle 204 moves in a positive direction in y-axis 112 and in a positive direction of x-axis 104, whereas a particle 206 moves in a positive direction in y-axis 112 and in a negative direction of x-axis 104. This is an example of anti-symmetrical motion.
To further the discussion, it should be noted that some thicknesses of materials may support many different modes of each type of anti-symmetrical and symmetrical Lamb waves. This will be described in greater detail with reference to FIG. 1 and additional reference to FIG. 3.
Returning to FIG. 1, a Lamb wave propagating from wave generating component 103 to receiving component 105 will propagate the distance d. By measuring the time of propagation tp, the velocity, V, of the Lamb wave may be calculated as:V=d/tp  (1)
Different modes of Lamb waves have different velocities through a common material. This will be described in further detail with reference to FIG. 3.
FIG. 3 illustrates a graph 300 of measured frequency versus measured group velocity for different modes of Lamb waves propagated through a 3.18 mm thick aluminum plate.
As shown in the figure, graph 300 includes a y-axis 302, an x-axis 304, functions 306, 308, 310, 312 and 314 and functions 316, 318, 320, 322 and 324, Y-axis 302 is a group velocity of a mode of Lamb wave and is measured in m/ms. X-axis 304 is the frequency of the vibration within the Lamb wave and is measured in MHz.
Functions 306, 308, 310, 312 and 314 each represent the frequency of vibration within a Lamb wave as a function of the group velocity of the Lamb wave for anti-symmetric modes. Functions 316, 318, 320, 322 and 324 are the frequency of vibration within a Lamb wave as a function of the group velocity of the Lamb wave for symmetric modes.
Generally speaking, the velocity of a Lamb wave is a function of the thickness of the material though which it is propagating and the frequency. With reference to FIG. 3, even though all modes travel through the same material, i.e., the same thickness of material, the different modes travel at different velocities.
As the frequency of the vibration increases, the number of modes, which the frequency supports, increases. At low frequencies, only a few modes may be supported. For example, at about 0.25 MHz, only mode 306 and mode 316 are supported. On the other hand, at a frequency of 1.5 MHz, mode 306, mode 316, mode 308, mode 318, mode 310 and mode 320 are supported.
Structural health monitoring (SHM) is important for detecting changes in the thickness of a material over time. Changes in thickness may be caused, for example, due to cracks or corrosion. If detected, cracks or corrosion, among other types of deterioration, may be treated by applying preventative maintenance to the material.
Conventionally, several methods have been used to monitor the structural health of a material. For example, ultrasonic transducers have been placed on the top and bottom surfaces of a material to detect changes in thickness of the material over time by analyzing ultrasonically generated Lamb waves.
However, it is difficult to place transducers in locations such that the transducer on the top surface of the material is precisely above the transducer on the bottom surface of the material. These offsets in positioning cause the thickness measurements from the ultrasonic waves to be inaccurate.
What is needed is a system and method which accurately conveys the thickness of a material. This system and method would be used to measure the thickness of a material at different points in time to determine the structural health of the material.